^{3}− 7

^{3}= 169. This is the square of an integer, namely 13, which can be expressed as 2

^{2}+ 3

^{2}.)

Welcome to BrainDen.com - Brain Teasers Forum. Like most online communities you must register to post in our community, but don't worry this is a simple free process. To be a part of BrainDen Forums you may create a new account or sign in if you already have an account. As a member you could start new topics, reply to others, subscribe to topics/forums to get automatic updates, get your own profile and make new friends. Of course, you can also enjoy our collection of amazing optical illusions and cool math games. If you like our site, you may support us by simply clicking Google "+1" or Facebook "Like" buttons at the top. If you have a website, we would appreciate a little link to BrainDen. Thanks and enjoy the Den :-) |

Guest Message by DevFuse

Started by BMAD, May 27 2013 12:00 AM

2 replies to this topic

Posted 27 May 2013 - 12:00 AM

Show that if the difference of the cubes of two consecutive integers is the square of an integer, then this integer is the sum of the squares of two consecutive integers.

(The smallest non-trivial example is: 8^{3} − 7^{3} = 169. This is the square of an integer, namely 13, which can be expressed as 2^{2} + 3^{2}.)

Posted 16 July 2013 - 10:49 AM

Spoiler for A start

Posted 17 July 2013 - 08:37 PM

Spoiler for some helpful info, perhaps

0 members, 0 guests, 0 anonymous users